In fact, our extension operator is “more universal” than the Rychkov extension \(E^R\)  [1]}. Although \(E^R\)  is bounded in all Besov and Triebel-Lizorkin spaces (see [1]}), it is not known whether \(E^R\)  is bounded on the endpoint Sobolev spaces \(W^{k,1}\) , \(W^{k,\infty }\)  and the \(C^k\) -spaces. On the other hand, our extension operator is also defined on the measurable function space \(L^p(\mathbb {R}^n_+)\)  for \(0<p<1\) , whose element may not be realized as a distribution on \(\mathbb {R}^n_+\) .
